%0 Thesis %1 hanel2015singular %A Hänel, André %C Stuttgart %D 2015 %K iadm from:elkepeter Hänel elastic analysis Dirichlet-to-Neumann %T Singular problems in quantum and elastic waveguides via Dirichlet-to-Neumann analysis. %X "The present work is concerned with the existence and the behaviour of discrete eigenvalues arising from a perturbation of an infinite waveguide in quantum mechanics or elasticity theory. Physically, eigenvalues correspond to bound states in quantum me-chanics or harmonic oscillations near imperfections such as cracks and holes in elasticity theory. They play an important role in applications in science and industry such as non-destructive testing theory of sensitive structures (e.g. wings of air planes, nuclear components etc.). More specifically we consider the asymptotic behaviour of the discrete eigenvalues for small perturbations which arise from a change of the boundary conditions on a small sub-set of the boundary. From the spectral-theoretic point of view this kind of perturbation is of particular interest since standard methods such as the Birman-Schwinger principle for handling additive perturbations of operators fail. To determine the asymptotic be-haviour of the discrete eigenvalues we shall use a pseudo-differential approach which is based on an analysis of the corresponding Dirichlet-to-Neumann operator. This method is of benefit mainly because it uses the symbol expansion of the Dirichlet-to-Neumann operator in local charts and the behaviour of the resolvent near the spectral minimum. ... "

@phdthesis{hanel2015singular, abstract = {"The present work is concerned with the existence and the behaviour of discrete eigenvalues arising from a perturbation of an infinite waveguide in quantum mechanics or elasticity theory. Physically, eigenvalues correspond to bound states in quantum me-chanics or harmonic oscillations near imperfections such as cracks and holes in elasticity theory. They play an important role in applications in science and industry such as non-destructive testing theory of sensitive structures (e.g. wings of air planes, nuclear components etc.). More specifically we consider the asymptotic behaviour of the discrete eigenvalues for small perturbations which arise from a change of the boundary conditions on a small sub-set of the boundary. From the spectral-theoretic point of view this kind of perturbation is of particular interest since standard methods such as the Birman-Schwinger principle for handling additive perturbations of operators fail. To determine the asymptotic be-haviour of the discrete eigenvalues we shall use a pseudo-differential approach which is based on an analysis of the corresponding Dirichlet-to-Neumann operator. This method is of benefit mainly because it uses the symbol expansion of the Dirichlet-to-Neumann operator in local charts and the behaviour of the resolvent near the spectral minimum. ... "}, added-at = {2021-10-13T13:54:00.000+0200}, address = {Stuttgart}, author = {Hänel, André}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2caeb335741272a191839dd3fd993fcbe/mathematik}, interhash = {0279573e7b0ce47b72d05612f6ec0663}, intrahash = {caeb335741272a191839dd3fd993fcbe}, keywords = {iadm from:elkepeter Hänel elastic analysis Dirichlet-to-Neumann}, language = {English}, school = {Universität Stuttgart}, timestamp = {2021-10-13T11:54:00.000+0200}, title = {Singular problems in quantum and elastic waveguides via Dirichlet-to-Neumann analysis.}, type = {Dissertation}, year = 2015 }